Laser-induced electron localization in H$_2^+$: Mixed quantum-classical dynamics based on the exact time-dependent potential energy surface

摘要

We study the exact nuclear time-dependent potential energy surface (TDPES)for laser-induced electron localization with a view to eventually developing amixed quantum-classical dynamics method for strong-field processes. The TDPESis defined within the framework of the exact factorization [A. Abedi, N. T.Maitra, and E. K. U. Gross, Phys. Rev. Lett. 105, 123002 (2010)] and containsthe exact effect of the couplings to the electronic subsystem and to anyexternal fields within a scalar potential. We compare its features with thoseof the quasistatic potential energy surfaces (QSPES) often used to analysestrong-field processes. We show that the gauge-independent component of theTDPES has a mean-field-like character very close to the density-weightedaverage of the QSPESs. Oscillations in this component are smoothened out by thegauge-dependent component, and both components are needed to yield the correctforce on the nuclei. Once the localization begins to set in, the gradient ofthe exact TDPES tracks one QSPES and then switches to the other, similar to thedescription provided by surface-hopping between QSPESs. We show that evolvingan ensemble of classical nuclear trajectories on the exact TDPES accuratelyreproduces the exact dynamics. This study suggests that the mixedquantum-classical dynamics scheme based on evolving multiple classical nucleartrajectories on the exact TDPES will be a novel and useful method to simulatestrong field processes.